#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle_() continue; #define myceiling_(w) {ceil(w)} #define myhuge_(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZTGSY2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */ /* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, */ /* INFO ) */ /* CHARACTER TRANS */ /* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N */ /* DOUBLE PRECISION RDSCAL, RDSUM, SCALE */ /* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), */ /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTGSY2 solves the generalized Sylvester equation */ /* > */ /* > A * R - L * B = scale * C (1) */ /* > D * R - L * E = scale * F */ /* > */ /* > using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, */ /* > (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, */ /* > N-by-N and M-by-N, respectively. A, B, D and E are upper triangular */ /* > (i.e., (A,D) and (B,E) in generalized Schur form). */ /* > */ /* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */ /* > scaling factor chosen to avoid overflow. */ /* > */ /* > In matrix notation solving equation (1) corresponds to solve */ /* > Zx = scale * b, where Z is defined as */ /* > */ /* > Z = [ kron(In, A) -kron(B**H, Im) ] (2) */ /* > [ kron(In, D) -kron(E**H, Im) ], */ /* > */ /* > Ik is the identity matrix of size k and X**H is the conjuguate transpose of X. */ /* > kron(X, Y) is the Kronecker product between the matrices X and Y. */ /* > */ /* > If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b */ /* > is solved for, which is equivalent to solve for R and L in */ /* > */ /* > A**H * R + D**H * L = scale * C (3) */ /* > R * B**H + L * E**H = scale * -F */ /* > */ /* > This case is used to compute an estimate of Dif[(A, D), (B, E)] = */ /* > = sigma_min(Z) using reverse communication with ZLACON. */ /* > */ /* > ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL */ /* > of an upper bound on the separation between to matrix pairs. Then */ /* > the input (A, D), (B, E) are sub-pencils of two matrix pairs in */ /* > ZTGSYL. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > = 'N': solve the generalized Sylvester equation (1). */ /* > = 'T': solve the 'transposed' system (3). */ /* > \endverbatim */ /* > */ /* > \param[in] IJOB */ /* > \verbatim */ /* > IJOB is INTEGER */ /* > Specifies what kind of functionality to be performed. */ /* > =0: solve (1) only. */ /* > =1: A contribution from this subsystem to a Frobenius */ /* > norm-based estimate of the separation between two matrix */ /* > pairs is computed. (look ahead strategy is used). */ /* > =2: A contribution from this subsystem to a Frobenius */ /* > norm-based estimate of the separation between two matrix */ /* > pairs is computed. (DGECON on sub-systems is used.) */ /* > Not referenced if TRANS = 'T'. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > On entry, M specifies the order of A and D, and the row */ /* > dimension of C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > On entry, N specifies the order of B and E, and the column */ /* > dimension of C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA, M) */ /* > On entry, A contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the matrix A. LDA >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX*16 array, dimension (LDB, N) */ /* > On entry, B contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the matrix B. LDB >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is COMPLEX*16 array, dimension (LDC, N) */ /* > On entry, C contains the right-hand-side of the first matrix */ /* > equation in (1). */ /* > On exit, if IJOB = 0, C has been overwritten by the solution */ /* > R. */ /* > \endverbatim */ /* > */ /* > \param[in] LDC */ /* > \verbatim */ /* > LDC is INTEGER */ /* > The leading dimension of the matrix C. LDC >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is COMPLEX*16 array, dimension (LDD, M) */ /* > On entry, D contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDD */ /* > \verbatim */ /* > LDD is INTEGER */ /* > The leading dimension of the matrix D. LDD >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is COMPLEX*16 array, dimension (LDE, N) */ /* > On entry, E contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDE */ /* > \verbatim */ /* > LDE is INTEGER */ /* > The leading dimension of the matrix E. LDE >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] F */ /* > \verbatim */ /* > F is COMPLEX*16 array, dimension (LDF, N) */ /* > On entry, F contains the right-hand-side of the second matrix */ /* > equation in (1). */ /* > On exit, if IJOB = 0, F has been overwritten by the solution */ /* > L. */ /* > \endverbatim */ /* > */ /* > \param[in] LDF */ /* > \verbatim */ /* > LDF is INTEGER */ /* > The leading dimension of the matrix F. LDF >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE */ /* > \verbatim */ /* > SCALE is DOUBLE PRECISION */ /* > On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */ /* > R and L (C and F on entry) will hold the solutions to a */ /* > slightly perturbed system but the input matrices A, B, D and */ /* > E have not been changed. If SCALE = 0, R and L will hold the */ /* > solutions to the homogeneous system with C = F = 0. */ /* > Normally, SCALE = 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] RDSUM */ /* > \verbatim */ /* > RDSUM is DOUBLE PRECISION */ /* > On entry, the sum of squares of computed contributions to */ /* > the Dif-estimate under computation by ZTGSYL, where the */ /* > scaling factor RDSCAL (see below) has been factored out. */ /* > On exit, the corresponding sum of squares updated with the */ /* > contributions from the current sub-system. */ /* > If TRANS = 'T' RDSUM is not touched. */ /* > NOTE: RDSUM only makes sense when ZTGSY2 is called by */ /* > ZTGSYL. */ /* > \endverbatim */ /* > */ /* > \param[in,out] RDSCAL */ /* > \verbatim */ /* > RDSCAL is DOUBLE PRECISION */ /* > On entry, scaling factor used to prevent overflow in RDSUM. */ /* > On exit, RDSCAL is updated w.r.t. the current contributions */ /* > in RDSUM. */ /* > If TRANS = 'T', RDSCAL is not touched. */ /* > NOTE: RDSCAL only makes sense when ZTGSY2 is called by */ /* > ZTGSYL. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > On exit, if INFO is set to */ /* > =0: Successful exit */ /* > <0: If INFO = -i, input argument number i is illegal. */ /* > >0: The matrix pairs (A, D) and (B, E) have common or very */ /* > close eigenvalues. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16SYauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* > Umea University, S-901 87 Umea, Sweden. */ /* ===================================================================== */ /* Subroutine */ int ztgsy2_(char *trans, integer *ijob, integer *m, integer * n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd, doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf, doublereal *scale, doublereal *rdsum, doublereal *rdscal, integer * info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1, d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3, i__4; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; /* Local variables */ integer ierr, ipiv[2], jpiv[2], i__, j, k; doublecomplex alpha, z__[4] /* was [2][2] */; extern logical lsame_(char *, char *); extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zgesc2_( integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublereal *), zgetc2_(integer *, doublecomplex *, integer *, integer *, integer *, integer *); doublereal scaloc; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zlatdf_( integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, doublereal *, integer *, integer *); logical notran; doublecomplex rhs[2]; /* -- LAPACK auxiliary routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Decode and test input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; d_dim1 = *ldd; d_offset = 1 + d_dim1 * 1; d__ -= d_offset; e_dim1 = *lde; e_offset = 1 + e_dim1 * 1; e -= e_offset; f_dim1 = *ldf; f_offset = 1 + f_dim1 * 1; f -= f_offset; /* Function Body */ *info = 0; ierr = 0; notran = lsame_(trans, "N"); if (! notran && ! lsame_(trans, "C")) { *info = -1; } else if (notran) { if (*ijob < 0 || *ijob > 2) { *info = -2; } } if (*info == 0) { if (*m <= 0) { *info = -3; } else if (*n <= 0) { *info = -4; } else if (*lda < f2cmax(1,*m)) { *info = -6; } else if (*ldb < f2cmax(1,*n)) { *info = -8; } else if (*ldc < f2cmax(1,*m)) { *info = -10; } else if (*ldd < f2cmax(1,*m)) { *info = -12; } else if (*lde < f2cmax(1,*n)) { *info = -14; } else if (*ldf < f2cmax(1,*m)) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZTGSY2", &i__1, (ftnlen)6); return 0; } if (notran) { /* Solve (I, J) - system */ /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */ /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */ /* for I = M, M - 1, ..., 1; J = 1, 2, ..., N */ *scale = 1.; scaloc = 1.; i__1 = *n; for (j = 1; j <= i__1; ++j) { for (i__ = *m; i__ >= 1; --i__) { /* Build 2 by 2 system */ i__2 = i__ + i__ * a_dim1; z__[0].r = a[i__2].r, z__[0].i = a[i__2].i; i__2 = i__ + i__ * d_dim1; z__[1].r = d__[i__2].r, z__[1].i = d__[i__2].i; i__2 = j + j * b_dim1; z__1.r = -b[i__2].r, z__1.i = -b[i__2].i; z__[2].r = z__1.r, z__[2].i = z__1.i; i__2 = j + j * e_dim1; z__1.r = -e[i__2].r, z__1.i = -e[i__2].i; z__[3].r = z__1.r, z__[3].i = z__1.i; /* Set up right hand side(s) */ i__2 = i__ + j * c_dim1; rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i; i__2 = i__ + j * f_dim1; rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i; /* Solve Z * x = RHS */ zgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { zgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { z__1.r = scaloc, z__1.i = 0.; zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1); z__1.r = scaloc, z__1.i = 0.; zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1); /* L10: */ } *scale *= scaloc; } } else { zlatdf_(ijob, &c__2, z__, &c__2, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ i__2 = i__ + j * c_dim1; c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i; i__2 = i__ + j * f_dim1; f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i; /* Substitute R(I, J) and L(I, J) into remaining equation. */ if (i__ > 1) { z__1.r = -rhs[0].r, z__1.i = -rhs[0].i; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = i__ - 1; zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &c__[j * c_dim1 + 1], &c__1); i__2 = i__ - 1; zaxpy_(&i__2, &alpha, &d__[i__ * d_dim1 + 1], &c__1, &f[j * f_dim1 + 1], &c__1); } if (j < *n) { i__2 = *n - j; zaxpy_(&i__2, &rhs[1], &b[j + (j + 1) * b_dim1], ldb, & c__[i__ + (j + 1) * c_dim1], ldc); i__2 = *n - j; zaxpy_(&i__2, &rhs[1], &e[j + (j + 1) * e_dim1], lde, &f[ i__ + (j + 1) * f_dim1], ldf); } /* L20: */ } /* L30: */ } } else { /* Solve transposed (I, J) - system: */ /* A(I, I)**H * R(I, J) + D(I, I)**H * L(J, J) = C(I, J) */ /* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */ /* for I = 1, 2, ..., M, J = N, N - 1, ..., 1 */ *scale = 1.; scaloc = 1.; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { for (j = *n; j >= 1; --j) { /* Build 2 by 2 system Z**H */ d_cnjg(&z__1, &a[i__ + i__ * a_dim1]); z__[0].r = z__1.r, z__[0].i = z__1.i; d_cnjg(&z__2, &b[j + j * b_dim1]); z__1.r = -z__2.r, z__1.i = -z__2.i; z__[1].r = z__1.r, z__[1].i = z__1.i; d_cnjg(&z__1, &d__[i__ + i__ * d_dim1]); z__[2].r = z__1.r, z__[2].i = z__1.i; d_cnjg(&z__2, &e[j + j * e_dim1]); z__1.r = -z__2.r, z__1.i = -z__2.i; z__[3].r = z__1.r, z__[3].i = z__1.i; /* Set up right hand side(s) */ i__2 = i__ + j * c_dim1; rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i; i__2 = i__ + j * f_dim1; rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i; /* Solve Z**H * x = RHS */ zgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } zgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { z__1.r = scaloc, z__1.i = 0.; zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1); z__1.r = scaloc, z__1.i = 0.; zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1); /* L40: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ i__2 = i__ + j * c_dim1; c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i; i__2 = i__ + j * f_dim1; f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i; /* Substitute R(I, J) and L(I, J) into remaining equation. */ i__2 = j - 1; for (k = 1; k <= i__2; ++k) { i__3 = i__ + k * f_dim1; i__4 = i__ + k * f_dim1; d_cnjg(&z__4, &b[k + j * b_dim1]); z__3.r = rhs[0].r * z__4.r - rhs[0].i * z__4.i, z__3.i = rhs[0].r * z__4.i + rhs[0].i * z__4.r; z__2.r = f[i__4].r + z__3.r, z__2.i = f[i__4].i + z__3.i; d_cnjg(&z__6, &e[k + j * e_dim1]); z__5.r = rhs[1].r * z__6.r - rhs[1].i * z__6.i, z__5.i = rhs[1].r * z__6.i + rhs[1].i * z__6.r; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; f[i__3].r = z__1.r, f[i__3].i = z__1.i; /* L50: */ } i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { i__3 = k + j * c_dim1; i__4 = k + j * c_dim1; d_cnjg(&z__4, &a[i__ + k * a_dim1]); z__3.r = z__4.r * rhs[0].r - z__4.i * rhs[0].i, z__3.i = z__4.r * rhs[0].i + z__4.i * rhs[0].r; z__2.r = c__[i__4].r - z__3.r, z__2.i = c__[i__4].i - z__3.i; d_cnjg(&z__6, &d__[i__ + k * d_dim1]); z__5.r = z__6.r * rhs[1].r - z__6.i * rhs[1].i, z__5.i = z__6.r * rhs[1].i + z__6.i * rhs[1].r; z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L60: */ } /* L70: */ } /* L80: */ } } return 0; /* End of ZTGSY2 */ } /* ztgsy2_ */